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Use the arc length formula to find the length of the curve y = 7 − 4x, −1 ≤ x ≤ 2. Check your answer by noting that the curve is a line segment and calculating its length by the distance formula.

Use the arc length formula to find the length of the curve y = 7 − 4x, −1 ≤ x ≤ 2. Check your answer by noting that the curve is a line segment and calculating its length by the distance formula.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question

Use the arc length formula to find the length of the curve

y = 7 − 4x,
−1 ≤ x ≤ 2.

Check your answer by noting that the curve is a line segment and calculating its length by the distance formula.

This image displays a graph on the Cartesian coordinate system. The graph includes: - **Axes**: The horizontal axis is labeled as "x" and the vertical axis is labeled as "y." Both axes have markings at regular intervals, and there are grid lines to help identify specific points on the graph. - **Line Segment**: A blue line segment extends from the point (-1, 12) on the y-axis to the point (2, -2) on the x-axis. - **End Points**: The line segment begins at the coordinates (-1, 12) and ends at the coordinates (2, -2), indicating a negative slope. - **Grid**: The graph is overlaid with a grid that helps in identifying precise coordinates and measuring the slope of the line. This graphical representation could be used to teach concepts such as slope, coordinate plotting, and linear functions.
Transcribed Image Text:This image displays a graph on the Cartesian coordinate system. The graph includes: - **Axes**: The horizontal axis is labeled as "x" and the vertical axis is labeled as "y." Both axes have markings at regular intervals, and there are grid lines to help identify specific points on the graph. - **Line Segment**: A blue line segment extends from the point (-1, 12) on the y-axis to the point (2, -2) on the x-axis. - **End Points**: The line segment begins at the coordinates (-1, 12) and ends at the coordinates (2, -2), indicating a negative slope. - **Grid**: The graph is overlaid with a grid that helps in identifying precise coordinates and measuring the slope of the line. This graphical representation could be used to teach concepts such as slope, coordinate plotting, and linear functions.
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